There are 10 boys and 12 girls in the tennis club. The coach wants to select two players to practice first. Which statements are true? Check all that apply.
There is approximately a 27 percent likelihood that one boy and one girl will be chosen to practice first.
There is approximately a 52 percent likelihood that one boy and one girl will be chosen to practice first.
There is approximately a 19 percent likelihood that two boys will be chosen to practice first.
There is approximately a 19 percent likelihood that two girls will be chosen to practice first.
There is approximately a 29 percent likelihood that two girls will be chosen to practice first.

Since there are 22 participants all in all. The possible combinations of the two picked for practice first is,
22C2 = 231
The probability of picking one from each gender will be solved through the calculation below.
(10C1)x(12C1) / 231 = 40/77
In percentage, the answer would be approximately 52%. Thus, the answer is the first choice.

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oeerivona oeerivona · Answer 2 · 2022-01-21T13:38:08+01:00

Responses:

The true statements are;

There is approximately a 52 percent likelihood that one boy and one girl will be chosen to practice first

There is approximately a 19 percent likelihood that two boys will be chosen to practice first

There is approximately a 29 percent likelihood that two girls will be chosen to practice first

Methods used for the calculation of the probabilities

Number of boys = 10

Number of girls = 12

Total number of players = 10 + 12 = 22

Number of ways of selecting 2 players from 22 = ₂₂C₂ = 231

Number of ways of selecting a boy = ₁₀C₁ = 10

Number of ways of selecting a girl = ₁₂C₁ = 12

Number of ways of selecting one girl and one boy = ₁₀C₁ × ₁₂C₁ = 120

[tex]Likelihood \ that \ one \ girl \ and \ one \ boy \ will \ be \ chosen = \dfrac{120}{231} \approx \mathbf{ 52\%}[/tex]

Therefore;

The second statement is true

Number of ways of selecting 2 boys = ₁₀C₂ = 45

[tex]Likelihood \ that \ two \ boys \ chosen = \dfrac{45}{231} \approx \mathbf{ 19\%}[/tex]

Therefore;

The third statement is true

Number of ways of selecting 2 girls = ₁₂C₂ = 66

[tex]Likelihood \ two \ girls \ are \ chosen = \dfrac{66}{231} \approx \mathbf{ 29\%}[/tex]

Therefore;

The fifth statement is true

Learn more about the probability of an event here:

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