Mutually Exclusive - Or Not
A card is drawn from a standard deck
Event A:A spade is selected
Event B:A club is selected
Suppose you are about to draw a single card, at random, from a standard deck of 52 playing cards. Determine the probability:
a) You draw an 10 or a king
P(10 or King) = 8/52 or 15.4%
Definition: the probability of an event ( A ), given that another ( B ) has already occurred
What is conditional probability
Experiment (Independent or Dependent)
Choosing cards without replacement from a standard deck
Event A:First card is a king
Event B:Second card is a king
What is a dependent event
Experiment (mutually exclusive or non mutually exclusive)
Two coins are flipped
Event A: Both coins land on heads
Event B: Both coins lands on tails
What is "Mutually Exlcusive"
Suppose you are about to draw a single card, at random, from a standard deck of 52 playing cards. Determine the probability:
a) You draw a red card or a face
P(red or face card)= 26/52 +12/52 -6/52 = 32/52 = 61.5%
Jersey draws two cards from a deck of 52 cards without replacement. Are these events dependent or independent?
What is dependent
Experiment (Independent or Dependent)
Rolling a die and tossing a coin
Event A:Rolling 2 on the die
Event B:Tossing tails on the coin
What is an independent event
Experiment (mutually exclusive or non mutually exclusive)
A coin is flipped
Event A:The coin land on heads
Event B:The coin lands on tails
What is Mutually Exclusive
4) Mr. and Mrs. Tawil have had problems starting their two cars during the cold winter months. They decided to record the number of times each car starts during one month period in the winter. They attempted to start each car every morning for thirty days and recorded the following information:
What is the probability that on any particular morning during the month at least one of the cars starts?
P(car start) = 26/30 or 86.67%
Davis is drawing two cards from a deck of 52 playing cards without replacement. Determine the probability that both cards are red.
P(both red) = 26/52 * 25/51 = 24.5%
P(1,6) = 1/36
Experiment (mutually exclusive or non mutually exclusive)
A granola bar is chosen
Event A:The bar contains raisins
Event B:The bar contains nuts
What is non-mutually exclusive
The probability that John will study on Friday night is 0.6. The probability that he will play video games on Friday night is 0.8. The probability that he will do at least one of these activities is 0.8.
Determine the probability that he will do both activities
P(both activities)= 60%
Este has 6 toonies, 4 loonies and 3 quarters in his pocket. He's boasting to Mason that he only has toonies in his pocket. Mason asks Este to prove it. What are the odds in favor that Este pulls out two toonies at random. (Hint: Find the probability first)
Odds in favor
30:126
or 5:21
Classify the event as independent or dependent then find the probability that the events will occur: "A spinner with 5 equal coloured sections- red, blue, green, yellow and white- is spun twice in a row.
P(at least one red) = P(first red)+P(second Red)+P(both red)
= (1/5 *4/5)+(4/5*1/5)+(1/5*1/5)
=9/25 = 36%
Experiment (mutually exclusive or non mutually exclusive)
A card is drawn from a standard deck
Event A: A spade is selected
Event B:A black seven is selected
What is Non Mutually Exclusive
David is playing with an incomplete deck of cards. When one card is selected at random from the incomplete deck, the probability that it is a heart is 0.3 and the probability that it is a face card is 0.2. If the probability that the card is a heart and a face card is 0.1, calculate the probability that the card is a heart or a face card.
P(H or F) = One or the other, not both = 0.1 + 0.2 = 0.3 = 30%
Ryan's basketball team is playing a game tomorrow. Based on the team record, they have a 50% chance of winning if the price of gas is above $1.90/L, and a 20% chance of losing if the cost of gas is below or equal to $1.90/L. There's a 20% chance the the cost of gas will be above $1.90/L tomorrow.
Determine the probability that his team will lose tomorrow.
P (Loss) = 0.2*0.5 + 0.8*0.2 = 0.26 = 26% chance of losing
Design a spinner (how many sides/colours) so that when you roll a standard die and spin the spinner, the probability of rolling a multiple of 3 and spinning red is 1/24.
The spinner must have 8 sides