Question

The bag contains 7 red beads and 4 black beads. When we take a bead from the bag without looking.
a) What is the probability of it being red
b) Find the number of black beads to be put in the bag so that the probability of getting a black bead come .
1/2​

Answer 1

Answer:

(a) 7/11

(b) 3

Step-by-step explanation:

Total number of beads in the bag = 7 + 4 = 11 beads.

Number of Red beads = 7 beads.

Number of Black beads = 4 beads.

We know that;

$\sf \dashrightarrow \ Probability \ of \ an \ Event (E) = \dfrac{No \! : \ \! of \ favourable \ outcomes}{Total \ No \! : \ \! \! of \ Outcomes}$

Using this relation, we'll try to find out the probabilities of (a) and (b) happening.

___________________

(a) What is the probability of the bead being red?

Number of favourable outcomes/Number of White beads = 7

Total number of outcomes = 11

Let "E" be the probability of getting a red bead.

$\sf \dashrightarrow \ P(E) = \dfrac{No \! : \ \! of \ favourable \ outcomes}{Total \ No \! : \ \! \! of \ Outcomes}$

$\sf \dashrightarrow \ P(E) = \dfrac{7}{11}$

Therefore, the probability of getting a red bead is 7/11.

___________________

b) Find the number of black beads to be put in the bag so that the probability of getting a black bead comes 1/2​.

Let "E" be the probability of getting a black bead.

According to the question, P(E) should be equal to 12. Let the number of black beads that need to be added be "x".

No: of favourable outcomes/No: of black beads = 4 + x

Total number of outcomes = 11 + x

$\sf \dashrightarrow \ P(E) = \dfrac{No \! : \ \! of \ favourable \ outcomes}{Total \ No \! : \ \! \! of \ Outcomes + Extra \ black \ beads \ to \ be \ added}$

$\sf \dashrightarrow \ \dfrac{1}{2} = \dfrac{4 + x}{11 + x}$

Cross multiply;

$\sf \dashrightarrow \ 8 + 2x = 11 + x$

$\sf \dashrightarrow \ 2x - x = 11 - 8$

$\sf \dashrightarrow \ x = 3$

3 more black beads need to be added to the bag in order for P(E) to be equal to 1/2.

Answer 2

Given :-

The  bag contains 7 red beads and 4 black beads. When we take a bead from the bag without looking.

To Find :-

a) What is the probability of it being red

b) Find the number of black beads to be put in the bag so that the probability of getting a black bead come .

1/2​

Solution :-

We know that

$\bf Probability = \dfrac{Favorable \; outcomes}{Total \; outcomes}$

$\sf Probability = \dfrac{7}{7+4}$

$\sf Probability = \dfrac{7}{11}$

                                                                                   

Let the required outcomes be x

$\sf \dfrac{1}{2} = \dfrac{7+x}{11+ x}$

$\sf 11 + x=2(7+x)$

$\sf 11 +x=14+2x$

$\sf 11-14 = x-2x$

$\sf -3=-x$

$\sf 3 =x$