Probability questions below...please help and explain...7th grade math?

Question

Four Girls and eight boys are running for president or vice president of the student council. Find each probability

1. Find the probability that two boys are elected.
2. Find the probability that two girls are elected
3. Find the probability that the president is a boy and the vice president is a girl
4. Find the probability that the president is a girl and the vice president is a boy.

please give an explanation on how to do it. Thanks

Answer 1

In each case, you do the probability of one event (the president of the specified gender) and then multiply by the probability for the subsequent event. You have to account for the fact that the first event (for example a boy being elected president) changes the size and composition of the pool of people left over, who could be elected vice president.

1. There are 12 candidates, and 8 boys, so it's 8/12 for a boy to be president. That leaves 7 boys among 11 remaining candidates, for vice president. 8/12 * 7/11 = 14/33

2. There are 12 candidates, and 4 girls, so it's 4/12 for a girl to be president. That leaves 3 girls among 11 remaining candidates, for vice president. 4/12 * 3/11 = 3/33 = 1/11

3. There are 12 candidates, and 8 boys, so it's 8/12 for a boy to be president. That leaves 4 girls among 11 remaining candidates, for vice president. 8/12 * 4/11 = 8/33

4. 2. There are 12 candidates, and 4 girls, so it's 4/12 for a girl to be president. That leaves 8 boys among 11 remaining candidates, for vice president. 4/12 * 8/11 = 8/33

Since you are checking all four possible gender combinations for president/vice president, you can test your answers by checking the sum of (1) to (4) above should equal one:

14/33 + 3/33 + 8/33 + 8/33 =? 1
(14 + 3 + 8 + 8)/33 =? 1
33 / 33 =? 1
1 = 1

Answer 2

Probability a boy will be elected is 8/12
Probability a second boy will be elected is 7/11
So probability 2 boys elected is 8/12 *7/11= 56/132 =14/33

For girls this would be 4/12 *3/11= 3/33 =1/11

8/12*4/11= 8/33

4/12*8/11 =8/33

Answer 3

Its too complex to explain not in person. Ask your math teacher for extra help. Don't be embarrassed. It's a life skill that helps people succeed.