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As return gifts heena makes 4 pouches having 3 colored pencils and 4 erasers and 3 pouches having 5 colored pencils and 3 erasers. If a kid grabs one eraser from the pouch then what is the probability of it being from second set of pouch?

As return gifts heena makes 4 pouches having 3 colored pencils and 4 erasers and 3 pouches having 5 colored pencils and 3 erasers. If a kid grabs one eraser from the pouch then what is the probability of it being from second set of pouch? Correct Answer 63 / 191

Given:

4 pouches = 3 colored pencils +  4 erasers

3 pouches = 5 colored pencils + 3 erasers

Calculation:

Total pouches = 7

Total erasers in one pouch of first set and one pouch of second set = 7

Total elements in first set of pouch = 7

Total elements in second set of pouch = 8

Favorable events = Number of way selecting 2nd Bag × Number of ways selection 1 eraser from 2nd bag

Favorable events = (3 / 7) × (3 / 8)

Total events = Number of way selecting 2nd Bag × Number of ways selection 1 eraser from 2nd bag + Number of way selecting 1st Bag × Number of ways selection 1 eraser from 1st bag

Total events = ((3 / 7) × (3 / 8)) + ((4 / 7) × (4 / 7))

Probability = (9 / 56) / ((63 + 128)/ 392)

Probability = 9 × 392 / (56 × 191)

Probability = 63/ 191

∴ Probability of second eraser being from second set of pouch is 63/ 191

Key Points

Probability = Favorable events / Total events

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