use the complement of calculate the indicated probabilities. one pile of cards contains the number 2 through…

use the complement of calculate the indicated probabilities. one pile of cards contains the number 2 through 6 in red hearts. a second pile of cards contains the numbers 4 through 8 in black spades. each pile of cards has been randomly shuffled. if one card from each pile is chosen at the same time, what is the probability that the sum will be less than 12?

use the complement of calculate the indicated probabilities. one pile of cards contains the number 2 through 6 in red hearts. a second pile of cards contains the numbers 4 through 8 in black spades. each pile of cards has been randomly shuffled. if one card from each pile is chosen at the same time, what is the probability that the sum will be less than 12?

Answer

Explanation:

Step1: Find total outcomes

There are 5 cards in the first pile and 5 in the second, so total outcomes = 5×5 = 25.

Step2: Find outcomes with sum ≥ 12

Pairs are (6,6), (6,7), (6,8), (5,7), (5,8), (4,8), 6 pairs.

Step3: Use complement rule

P(sum < 12)=1 - P(sum ≥ 12)=1 - $\frac{6}{25}$=$\frac{19}{25}$

Answer:

$\frac{19}{25}$