Question

The probability that a person will get an electric contract is 2/5 and the probability that he will not get plumbing contract is 4/7.If the probability of getting atleast one contract is 2/3. What is the probability that he will get both?

plz answer!

Answer 1

Answer:

Step-by-step explanation:

eL. Contract=2/5

pL. Contract=3/7

Both sum=29/35

at least 1=2/3

both contract=29/35-2/3=17/105

so p=17/105

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Answer 2

Answer:

Probability that he will get both is   $\frac{17}{105}$

Step-by-step explanation:

Given: Probability that a person will get an electric contract is  $\frac{2}{5}$

          Probability that he will not get plumbing contract is  $\frac{4}{7}$

          probability of getting atleast one contract is  $\frac{2}{3}$

To find: Probability that he will get both, P(A∩B)

Let A be event that a person will get an electric contract and B be that he will get plumbing contract.

So, P(A) = $\frac{2}{5}$

    P(not B) =   $\frac{4}{7}$

    P(B) = 1 - P (not B) = $1-\frac{4}{7}$ =  $\frac{3}{7}$

    P(A or B) = P(A∪B) =  $\frac{2}{3}$

We use the following formula,

P(A∪B)  = P(A) + P(B) - P(A∩B)

P(A∩B) = P(A) + P(B) - P(A∪B)

P(A∩B) = $\frac{2}{5}+\frac{3}{7}-\frac{2}{3}$

P(A∩B) = $\frac{2\times21}{105}+\frac{3\times15}{105}-\frac{2\times35}{105}$

P(A∩B) = $\frac{42}{105}+\frac{45}{105}-\frac{70}{105}$

P(A∩B) = $\frac{42+45-70}{105}$

P(A∩B) = $\frac{17}{105}$

Therefore, Probability that he will get both is   $\frac{17}{105}$