Question

A packet contains 15 blue beads, 16 yellow beads and 19 orange beads. A bead is drawn at random from the packet. Find the probability that the bead drawn is:
1. an orange bead
2. a blue or a yellow bead

• A. (1)-19/50, (2)-31/50
• B. (1)- 8/25., (2)-31/50
• C. (1)- 8/25, (2)-1/50
• D. (1)- 7/50, (2)-31/50

Hint:

The probability of an event is calculated as \( \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \). For the probability of event A OR event B (mutually exclusive events), it's \( P(A \text{ or } B) = P(A) + P(B) \).

Answer 1

The Correct Option is A

Step 1: Calculate the total number of beads in the packet.
Number of blue beads = 15
Number of yellow beads = 16
Number of orange beads = 19
Total number of beads = Number of blue beads + Number of yellow beads + Number of orange beads \[ \text{Total number of beads} = 15 + 16 + 19 = 50 \] Step 2: Find the probability of drawing an orange bead.
Number of favorable outcomes (drawing an orange bead) = 19
Total number of possible outcomes (total beads) = 50
\[ P(\text{orange bead}) = \frac{\text{Number of orange beads}}{\text{Total number of beads}} = \frac{19}{50} \] Step 3: Find the probability of drawing a blue or a yellow bead.
Number of favorable outcomes (drawing a blue or a yellow bead) = Number of blue beads + Number of yellow beads \[ \text{Number of blue or yellow beads} = 15 + 16 = 31 \] Total number of possible outcomes (total beads) = 50 \[ P(\text{blue or yellow bead}) = \frac{\text{Number of blue or yellow beads}}{\text{Total number of beads}} = \frac{31}{50} \] Thus, the probabilities are:
1. Probability of drawing an orange bead = \( \frac{19}{50} \)
2. Probability of drawing a blue or a yellow bead = \( \frac{31}{50} \)
Comparing these results with the given options, option (A) matches.