Question

Q11. There are a large number of white beads in a bag. There are only white beads in the bag. Felicity wants to find an estimate for the number of beads in the bag. Felicity replaces 30 of the white beads in the bag with 30 black beads. She then takes 50 beads from the bag. 2 of the 50 beads are black. Felicity then puts the 50 beads back in the bag.

(a) Work out an estimate for the number of beads in the bag.​

Answer 1

we know that all the beads in the bag are white the initial number of beads in the bag is equal to the total number of white beads.

When Felicity replaces 30 white beads with 30 black beads, the total number of beads in the bag remains the same. So, the initial number of beads in the bag is equal to the final number of beads in the bag after this replacement.

Then Felicity takes 50 beads from the bag and finds that 2 of them are black. This means that of the 50 beads she took, 2/50 = 1/25 are black. It can therefore be estimated that the proportion of black beads in the bag is also 1/25.

Felicity then puts the 50 beads back in the bag, which does not change the proportion of black beads in the bag.

. If 1/25 of the beads in the bag are black, this means that the proportion of black beads in the bag is also 1/25.

1/25 of the total number of beads in the bag corresponds to the number of black beads.

Using this proportion, we can establish the following equation:

(1/25) = 30/N

where N is the total number of beads in the bag.

we resout

2N = 50 ×30

2N = 1500

N = 1500/2

N = 750

Estimated number of beads in bag: 750.

Explanation: