Question

If p(A)=x/3 and p(Ā)=2/5, then find x​

Answer 1

Step-by-step explanation:

Given:p(A)=x/3 and p(Ā)=2/5

To find: Value of x

Solution:

Tip: Probability of happening of an event 'p(A)' and not happening of the same event 'p(Ā)' add to one.

i.e.

P(A)+P(Ā)=1

Step 1: Add both probabilities and equate to 1

$\frac{x}{3} + \frac{2}{5} = 1$

Step 2: Take 2/5 to RHS and solve

$\frac{x}{3} = 1 - \frac{2}{5} \\ \\ \frac{x}{3} = \frac{5 - 2}{5} \\ \\ \frac{x}{3} = \frac{3}{5}$

Step 3: Cross multiply 3 to other side

$x = \frac{3 \times 3}{5} \\ \\ x = \frac{9}{5}$

Final answer:

$\bold{\red{x = \frac{9}{5}}}$

Verification:

P(A)+P(Ā)=1

Put value of x in LHS

$= \frac{ \frac{9}{5} }{3} + \frac{2}{5} \\ \\ = \frac{9}{15} + \frac{2}{5} \\ \\ = \frac{9 + 2 \times 3}{15} \\ \\ = \frac{9 + 6}{15} \\ \\ = \frac{15}{15} \\ \\ = 1 \\ \\ = RHS$

Hence Proved.

Hope it helps you.

To learn more on brainly:

1) find the the value of x if 3^2x+1=243

https://brainly.in/question/38428028

Answer 2

Answer:

Step-by-step explanation:

Given:p(A)=x/3 and p(Ā)=2/5

To find: Value of x

Solution:

Tip: Probability of happening of an event 'p(A)' and not happening of the same event 'p(Ā)' add to one.

i.e.

P(A)+P(Ā)=1

Step 1: Add both probabilities and equate to 1

$\frac{x}{3} + \frac{2}{5} = 1$

Step 2: Take 2/5 to RHS and solve

$\frac{x}{3} = 1 - \frac{2}{5} \\ \frac{x}{3} = \frac{5 - 2}{5} \\ \frac{x}{3} = \frac{3}{5}$

Step 3: Cross multiply 3 to other side

$x = \frac{3×3}{5} \\ x = \frac{9}{5}$

Final answer:

$x = \frac{9}{5}$