127k views
0 votes
If

there are 8 bolt are US spec and 6 bolts are shorts , what is the
probability of selecting either a US spec or a short bolt? (hint:
P(US U Short)

1 Answer

4 votes
To find the probability of selecting either a US spec or a short bolt, we need to calculate the union of the two events: US spec (denoted as US) and short (denoted as S). The probability of the union is denoted as P(US U S).

The formula for the union of two events is:

P(US U S) = P(US) + P(S) - P(US ∩ S)

Given that there are 8 US spec bolts and 6 short bolts, we can calculate the individual probabilities:

P(US) = 8 / (8 + 6) = 8 / 14 = 4 / 7

P(S) = 6 / (8 + 6) = 6 / 14 = 3 / 7

Now, we need to determine the probability of the intersection of the two events, P(US ∩ S). Since a bolt cannot be both US spec and short, the intersection is empty, and therefore P(US ∩ S) = 0.

Plugging in the values, we can calculate the probability of selecting either a US spec or a short bolt:

P(US U S) = P(US) + P(S) - P(US ∩ S)
= 4/7 + 3/7 - 0
= 7/7
= 1

Therefore, the probability of selecting either a US spec or a short bolt is 1, which means it is guaranteed to happen since it includes all the bolts available.
User WTEDST
by
7.8k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories