Question

A jar contains four blue marbles and two red marbles. suppose you choose a marble at random, and do not replace it. then you choose a second marble. find the probability of each event to the nearest tenth of a percent.

a.the first marble is blue and the second is red
b.both marbles are blue

Answer 1

A) 26.7%
B) 40%

The probability of A is given by 4/6(2/5), since this is done without replacement; there are 4 blue marbles out of 6. When the first one is gone, there are 2 red out of 5 remaining.

The probability of B is given by 4/6(3/5), since this is done without replacement; there are 4 blue marbles out of 6. When the first one is gone, there are 2 blue out of 5 remaining.

Answer 2

a)
`(4)/(15)`

b)
`(2)/(5)`

Explanation:

We are given the following information:

Number of red marbles in jar = 2

Number of blue marbles in jar = 4

Total number of marbles in jar = 6

Marbles are drawn from jar without replacement.

Formula:

`\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}`

a) Probability(First marble is blue and second is red)

=Probability(Drawing a blue marble in first draw) × Probability(Drawing a red marble in second draw)

`=(4)/(6)* (2)/(5)\\\\=(4)/(15)`

b) Probability(First marble is blue and second is also blue)

=Probability(Drawing a blue marble in first draw) × Probability(Drawing a blue marble in second draw)

`=(4)/(6)* (3)/(5)\\\\=(2)/(5)`