A class has 100 students, 70 of which are boys. 70% of the boys are involved in sports, while 40% of the girls are involved in sports. A student is chosen at random. If the student chosen is a boy, what is the probability that he is involved in sports?
Well if of 100 students there is 70 boys, and only 70% of the boys are in sports, all you need to do is find 70% of 70. Which is 49.
70 x 0.07= 4.9
4.9x10=49
To find the probability that a randomly chosen boy is involved in sports, we need to use conditional probability. Conditional probability calculates the likelihood of an event happening based on the occurrence of another event.
Let's break down the problem step by step:
Step 1: Calculate the probability that a student chosen at random is a boy.
Out of 100 students, we know that 70 are boys. So, the probability of choosing a boy is calculated by dividing the number of boys (70) by the total number of students (100):
Probability (boy) = Number of boys / Total number of students = 70/100 = 0.7
Step 2: Calculate the probability that a student chosen at random is involved in sports.
We are given that 70% of the boys are involved in sports, which means that 70% of 70 boys are involved in sports:
Probability (boy involved in sports) = 70% of 70 boys = (0.70)(70) = 49 boys involved in sports out of 100 students.
Step 3: Use the conditional probability formula to determine the probability that a randomly chosen boy is involved in sports.
The conditional probability formula is given by:
P(A|B) = P(A and B) / P(B)
Where P(A|B) represents the probability of event A happening, given that event B has occurred, P(A and B) is the probability of both A and B happening simultaneously, and P(B) is the probability of event B happening.
In our case, event A is the boy being involved in sports, and event B is selecting a boy.
Let's substitute the values:
P(A|B) = P(boy involved in sports) / P(boy)
P(A|B) = 49 boys involved in sports / 70 boys
P(A|B) = 49/70
P(A|B) ≈ 0.7
So, the probability that a randomly chosen boy from the class is involved in sports is approximately 0.7, or 70%.