A solid-fuel booster engine has been test-fired 2860 times. On 429 occasions, the engine failed to...

 

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A solid-fuel booster engine has been test-fired 2860 times. On 429 occasions, the engine failed to ignite. If a projectile is fitted with three identical and independent booster engines of this type, what is the probability on launching the projectile that a) All the engines fail to ignite, and b) At least one of the engine fails to ignite. A solid-fuel booster engine has been test-fired 2860 times. On 429 occasions, the engine failed to ignite. If a projectile is fitted with three identical and independent booster engines of this type, what is the probability on launching the projectile that a) All the engines fail to ignite, and b) At least one of the engine fails to ignite.