Question

a laundry bag contains 6 brown socks and 4 black socks, find the probability of picking a 2 brown socks, if the first sock is returned in the bag before the second sock is picked

Answer 1

ANSWER-

The probability of picking a brown sock on the first draw is 6/10, since there are 6 brown socks out of 10 total socks. Since the first sock is returned to the bag, the number of brown socks and black socks remain the same for the second draw.

The probability of picking a brown sock on the second draw, given that a brown sock was picked on the first draw, is also 6/10.

To find the probability of picking 2 brown socks, we can multiply the probability of picking a brown sock on the first draw by the probability of picking a brown sock on the second draw:

P(2 brown socks) = (6/10) x (6/10) = 36/100 = 0.36

Therefore, the probability of picking 2 brown socks, if the first sock is returned to the bag before the second sock is picked, is 0.36 or 36%.

Answer 2

The probability of picking a brown sock on the first draw is 6/10. Since the sock is returned to the bag, the number of socks and the number of brown socks remains the same for the second draw, so the probability of picking a brown sock on the second draw is also 6/10.

The probability of picking two brown socks is the product of the probabilities of picking a brown sock on the first draw and on the second draw, which is:

P(2 brown socks) = P(brown on first draw) * P(brown on second draw)

= 6/10 * 6/10

= 36/100

= 0.36

Therefore, the probability of picking two brown socks, if the first sock is returned in the bag before the second sock is picked, is 0.36 or 36%.