Question

question 9(multiple choice worth 2 points) (likelihood mc)
three softball players discussed their batting averages after a game.

	probability
player 2	$\frac{5}{9}$
player 3	$\frac{4}{7}$

compare the probabilities and interpret the likelihood. which statement is true?
player 1 is more likely to hit the ball than player 2 because p(player 1) > p(player 2)
player 2 is more likely to hit the ball than player 1 because p(player 2) > p(player 1)
player 3 is more likely to hit the ball than player 1 because p(player 3) > p(player 1)
player 2 is more likely to hit the ball than player 3 because p(player 2) > p(player 3)
question 10(multiple choice worth 2 points) (experimental probability mc)
a student randomly draws a card from a standard deck of 52 cards. he records the type of card drawn and

Explanation:

Step1: Find a common denominator

The common - denominator of 10, 9 and 7 is \(10\times9\times7 = 630\).

Step2: Convert the fractions

For Player 1: \(\frac{6}{10}=\frac{6\times63}{10\times63}=\frac{378}{630}\)
For Player 2: \(\frac{5}{9}=\frac{5\times70}{9\times70}=\frac{350}{630}\)
For Player 3: \(\frac{4}{7}=\frac{4\times90}{7\times90}=\frac{360}{630}\)

Step3: Compare the fractions

Since \(\frac{378}{630}>\frac{350}{630}>\frac{360}{630}\), we have \(\frac{6}{10}>\frac{5}{9}>\frac{4}{7}\), which means \(P(\text{Player }1)>P(\text{Player }2)>P(\text{Player }3)\)

Answer:

Player 1 is more likely to hit the ball than Player 2 because \(P(\text{Player }1)>P(\text{Player }2)\)