A probability experiment will consist of selecting one of two stacks of cards, and then choosing a card at random from the stack
. The first stack of cards consists of six red and five blue cards. The second stack of cards consists of nine red cards (and no blue cards). The probability experiment proceeds as follows: A fair die is rolled. If a 1 is rolled, the first stack is selected and if any other number is rolled, the second stack (the all-red one) is selected. Then a card is selected at random from whichever stack is selected. Suppose the card is red. What is the probability it came from the first stack
The probability that the red card came from the first stack is:
40%
Step-by-step explanation:
a) Data and Calculations:
Stack Red Blue Total
First 6 5 11
Second 9 0 9
Total 15 5 20
The probability of selecting from the first stack = 50% since equal opportunity is given to the two sacks.
The probability of red card from the first stack = 6/15 = 0.4 = 40%.
b) The probability that the red card came from the first stack is given by the number of red cards in the first stack divided by the number or red cards in the two stacks. This is equal to 6/15 = 0.4 or 40%.
