Question

A box contains 8 black beads and 12 white beads. Another box contains 9 black beads and 6
white beads. One bead from each box is taken.
(a) What is the probability that both beads are black?
(b) What is the probability of getting one black bead and one white bead?​

Answer 1

Answer:

a =17/35

b = 3/7

Step-by-step explanation:

solution----->

Given:-

• box A = 8 black beads and 12 white beads
• Box B = 9black and 6 white beads

as per condition

S = {B,B,B,B,B,B,B,W,W,W,W,W,W,W,W,W,W,W,W

B,B,B,B,B,B,B,B,B,W,W,W,W,W,W}

n (s)= 35

now as per first condition

A = {B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B,B}

n (A)= 17

$p = \frac{n(a)}{n(s)} \\ \\ p = \frac{17}{35}$

acording to 2nd condition

B ={B,B,B,B,B,B,B,B,W,W,W,W,W,W}

n (B)= 15

$p = \frac{n(b)}{n(s)} \\ \\ p = \frac{15}{35} \\ \\ p = \frac{3}{7}$

Answer 2

The probability that both beads are black is 6/25 and getting one bead black and one white is 13/25.

• Given:

First box contains 8 black beads and 12 white beads and second contains 9  black box and 6 white beads.

One bead from each box is taken .

(a)Both bead boxes are black

Number of such cases where both the beads are black = 9×8 = 72.

Total number of cases = 20×15 = 300

Now, probability = 72/300 = 6/25.

(b) one bead box is black and one bead box is white

Number of such cases = 8×6 + 12×9 = 48 + 108 = 156

Total number of possibilities = 20 × 15 = 300

Probability = 156 / 300 = 13/25