So let's first define our events:

let $A$ be the event that a product was supplied by company A

let $B$ be the event that a product was supplied by company B

let $D$ be the event that a product is defective

Translated to our symbols, the problem provides us with the following information:

$P(A) = 0.60$

$P(B) = 0.40$

$P(D|A) = 0.05$

$P(D|B) = 0.01$

Where | means "given that".

a) $P(B \cap D)$ (the $\cap$ means "and")

From the multiplication rule we know that $P(B \cap D) = P(D|B)P(B)$, both of which are given.

So we have $P(B \cap D) = 0.40 * 0.01 = 0.004$

b) $P(D)$

For this we can use the law of total probability, partitioning the sample space into defects given A and defects given B to arrive at the total probability of a defect from any given.

$P(D) = P(D|A)P(A) + P(D|B)P(B) = 0.05*0.60 + 0.01 * 0.40 = 0.034$

c) $P(B|D)$

For this we can use Bayes' rule of conditional probability, which states that

$P(B|D) = \frac{P(D|B)P(B)}{P(D)}$

Everything in the numerator is given, we calculated the denominator in part b), so now it's just a matter of plugging in the numbers.

$P(B|D) = \frac{0.01*0.40}{0.034} = 0.118$

Hopefully that answers everything!