Question

A tool box contains 40 bolts, 14 Hex bolts, 16 Anchor bolts and 10 Machine bolts. 3 bolts are randomly selected from the tool box, one after the other, the first bolt is not being replaced before the second is selected. Find the following probabilities: P (Hex bolt, Anchor bolts and Machine bolts in that order). P (Hex bolt, Anchor bolts and Machine bolts in any order). P (3 different type of bolts).

Answer 1

The probabilities here are computed as:
P(Hex bolt, Anchor Bolts, and Machine bolts)

= P(Hex bolt)P(Anchor bolt given that Hex bolt has been taken out)P(Machine bolts given that Hex and Anchor bolts are taken out)

Total bolts = 40

Therefore, the probability here is computed as:
= (14/40)*(16/39)*(10/38)
= 0.0378

Therefore 0.0378 is the required probability here.

b) P(3 different types of bolts)

= P(Hex bolt, Anchor Bolts, and Machine bolts) * Number of permutations of the 3 bolts

= 0.0378*3!

= 0.2268

Therefore 0.2268 is the required probability here.